To understand the molecular logic of a cell, methods of modeling and simulation are important. The primary motivation for using computer-aided study mechanisms is that observing biochemical systems and conducting experiments on them is difficult. Yet, such observation and experimentation can be necessary to improve health care. For example, the study of gene regulatory and metabolic networks plays an important role in the detection of genetic or metabolic defects, as well as in therapeutic research on pharmaceutical formulations. Genetic and metabolic defects often lead to diseases like high blood pressure, Alzheimer's, cancer, and diabetes. Biochemical models can be used to integrate detailed biochemical data, and to help understand the behavior of complex systems of molecular interactions. Building such biochemical models has remained an art and an arduous task.
Many processes in molecular biology, as well as other biochemical systems, demonstrate a stochastic nature. Such biological phenomena necessitate the use of stochastic models. The primary difference between deterministic and stochastic models is that in a deterministic model an initial condition results in one, and only one, final outcome, whereas in a stochastic model distinct final outcomes can arise from identical initial conditions. Therefore, the theoretical understanding of molecular and developmental biology using computational systems has to account for variations caused by the stochastic interactions of molecules and other reactants, as well as the large variety of these molecules and the complex feedback loops characterizing biochemical systems. Traditional mathematical tools are not well suited to modeling such dynamic behavior.
One type of mathematical formalism that has been applied to biochemical systems is the Petri-net. The Petri-net formalism is a graphically oriented language of design, specification, simulation, and verification of systems. It offers methods to represent the structure of a discrete-event system, to simulate the system's behavior, and to draw certain types of general conclusions regarding the properties of the system. Simple Petri-net models, however, do not provide features that can capture quantitative aspects of stochastic biochemical systems.
However, the reference P J E Goss and Peccoud, “Quantitative modeling of stochastic systems in molecular biology using stochastic Petri-nets,” in Proceedings of the National Academy of Sciences, USA, vol. 95, pp. 6750-6755 (June 1998) [hereinafter Goss and Peccoud], describes an extended Petri-net formalism having features that allow for the modeling of stochastic biochemical systems. Such augmented Petri-net frameworks may be referred to as spatially homogenous stochastic Petri-net frameworks, and have been successfully applied to the modeling and simulation of many complex biological and other biochemical systems.
A significant drawback of the spatially homogenous stochastic Petri-net framework described in [Goss and Peccoud] is its inability to represent space heterogeneously, and hence its inability to model effects resulting from non-uniform spatial distributions of interacting molecules and other reactants. In other words, current Petri-net frameworks are unable to model systems existing within spatially heterogeneous spaces, in which biochemical reactants are non-uniformly spatially distributed. For this and other reasons, therefore, there is a need for the present invention.